Question

directions: if l || m, solve for x.
5.
6.
7.
8.

Explanation:

Step1: Use vertical - angle property for problem 5

Vertical angles are equal. So, $9x + 2=119$.

Step2: Solve the equation for $x$ in problem 5

Subtract 2 from both sides: $9x=119 - 2=117$. Then divide both sides by 9: $x = \frac{117}{9}=13$.

Step3: Use corresponding - angle property for problem 6

Corresponding angles are equal when two lines are parallel. So, $12x-8 = 104$.

Step4: Solve the equation for $x$ in problem 6

Add 8 to both sides: $12x=104 + 8=112$. Then divide both sides by 12: $x=\frac{112}{12}=\frac{28}{3}$.

Step5: Use alternate - interior angles property for problem 7

Alternate - interior angles are equal when two lines are parallel. So, $5x + 7=8x-71$.

Step6: Solve the equation for $x$ in problem 7

Subtract $5x$ from both sides: $7=8x-5x - 71$, which simplifies to $7 = 3x-71$. Add 71 to both sides: $3x=7 + 71=78$. Then divide both sides by 3: $x = 26$.

Step7: Use same - side interior angles property for problem 8

Same - side interior angles are supplementary when two lines are parallel. So, $(7x-61)+(4x - 7)=180$.

Step8: Simplify the left - hand side of the equation in problem 8

Combine like terms: $7x+4x-61 - 7=180$, which gives $11x-68 = 180$.

Step9: Solve the equation for $x$ in problem 8

Add 68 to both sides: $11x=180 + 68=248$. Then divide both sides by 11: $x=\frac{248}{11}$.

Answer:

1. $x = 13$
2. $x=\frac{28}{3}$
3. $x = 26$
4. $x=\frac{248}{11}$